| utf25-007 Let $ f( x)=2x+\log_e x$ for $x>0$.
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| utf28-001 Derive the formulas below. {(Hint: differentiate $g(g^{{-1}}(x))=x$ then use triangles (e.g. you know that $\arcsin x$ is an angle, $\theta$, whose sine is $x$.).)} $$a) \frac{ds}{dx}{\arccos x}=\frac{-1 }{ \sqrt {1-x^2}} b) \frac{ds}{dx}{\arctan x}= \frac{1 }{ 1+x^2} $$ |
| utf28-003 Differentiate each of the following functions. $$a) f( x) = \arctan (\arctan (\arctan x)) b) f( x) = \arcsin (\arctan (\arccos x))$$ |
| utf28-004
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| utf28-008 Find all continuous functions $ f( x)$ which satisfy the equation $$( f( x))^2 = \int_{0}^{x}{{ f( t) \frac{t}{ 1+t^2}}} dt.$$ |